To identify the key features of the graph of the function \( f(x) \), we need to analyze the general shape and specified values of the graph at various points, based on the vertical and horizontal values given (0 through 11) and the output values (0 through approximately 2).
Since I cannot see the graph, I will provide a general method to find the keys features and examples based on standard quadratic or other common forms of functions.
Part A: Identify Key Features of the Graph
A. Vertex: The vertex of a parabola (assuming \( f(x) \) is a quadratic function) can be found at the highest or lowest point of the graph. If you have the coordinates from the graph, you can identify this directly.
B. Axis of symmetry: The axis of symmetry for a parabola is the vertical line that passes through the vertex. If the vertex is at \( (a, b) \), the axis of symmetry would be \( x = a \).
C. y-intercept: The y-intercept of the function is the value of \( f(x) \) when \( x = 0 \). You can find this point from the graph where it crosses the y-axis.
D. x-intercepts: The x-intercepts are the points where the function is equal to zero (where the graph crosses the x-axis). These can be taken in order, left to right.
Assuming a simple scenario, if you refer to the values provided (0 through 11 on x and corresponding f(x) values):
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Vertex: Let's say your graph peaks at \( x = 5 \) and \( f(5) = 1.75 \), the vertex would be \( (5, 1.75) \).
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Axis of symmetry: If the vertex is at \( x = 5 \), the axis of symmetry is \( x = 5 \).
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y-intercept: If the graph crosses the y-axis at \( (0, 1) \), you have \( (0, 1) \) for the y-intercept.
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x-intercepts: If your graph crosses the x-axis at two points, for example, \( (2, 0) \) and \( (8, 0) \), you would list these as the x-intercepts.
With specific numbers from your graph, fill in the details:
A. Vertex: (5, 1.75)
B. Axis of symmetry: x = 5
C. y-intercept: (0, 1)
D. x-intercepts from left to right: (2, 0) and (8, 0)
Please replace values with actual ones from the graph you have.